#	Seifert-Weber Dodecahedral Space
#
#	To construct the Seifert-Weber space, take
#	a regular hyperbolic dodecahedron of dihedral angle 2π/5 and
#	glue pairs of opposite faces with a consistent 3/5 twist.
#	The matrices below give all right-handed twists, but
#	all left-handed ones would be just as good.
#
#	In terms of the golden ratio φ = (√5 + 1)/2,
#	the matrix entries are
#
#		φ/2             = (√5 + 1)/4         ≈ 0.80901...
#		(φ - 1)/2       = (√5 - 1)/4         ≈ 0.30901...
#		φ/2 + 1         = (√5 + 5)/4         ≈ 1.80901...
#		φ + 1           = (√5 + 3)/2         ≈ 2.61803...
#		√(7φ + 3) / 2   = √(13/8 + 7(√5)/8)  ≈ 1.89250...
#		√(17φ + 10) / 2 = √(37/8 + 17(√5)/8) ≈ 3.06213...
#		2φ + 1/2        = √5 + 3/2           ≈ 3.73606...
#
#	To express the matrix entries as elements of a field Q[ξ], where
#	ξ is the root of a fourth-degree polynomial, please see
#	the Mathematica notebook “primitive elements for Seifert-Weber.nb”.

 0.80901699437494742410 -0.80901699437494742410  1.80901699437494742410  1.89250085345088179814
 0.80901699437494742410 -0.30901699437494742410 -0.50000000000000000000  0.00000000000000000000
 1.80901699437494742410  0.50000000000000000000  2.61803398874989484820  3.06213070462171047818
 1.89250085345088179814  0.00000000000000000000  3.06213070462171047818  3.73606797749978969641

 0.80901699437494742410  0.80901699437494742410 -1.80901699437494742410  1.89250085345088179814
-0.80901699437494742410 -0.30901699437494742410 -0.50000000000000000000  0.00000000000000000000
-1.80901699437494742410  0.50000000000000000000  2.61803398874989484820 -3.06213070462171047818
 1.89250085345088179814  0.00000000000000000000 -3.06213070462171047818  3.73606797749978969641

 0.80901699437494742410 -0.80901699437494742410 -1.80901699437494742410 -1.89250085345088179814
 0.80901699437494742410 -0.30901699437494742410  0.50000000000000000000  0.00000000000000000000
-1.80901699437494742410 -0.50000000000000000000  2.61803398874989484820  3.06213070462171047818
-1.89250085345088179814  0.00000000000000000000  3.06213070462171047818  3.73606797749978969641

 0.80901699437494742410  0.80901699437494742410  1.80901699437494742410 -1.89250085345088179814
-0.80901699437494742410 -0.30901699437494742410  0.50000000000000000000  0.00000000000000000000
 1.80901699437494742410 -0.50000000000000000000  2.61803398874989484820 -3.06213070462171047818
-1.89250085345088179814  0.00000000000000000000 -3.06213070462171047818  3.73606797749978969641

-0.30901699437494742410 -0.50000000000000000000  0.80901699437494742410  0.00000000000000000000
 0.50000000000000000000  2.61803398874989484820  1.80901699437494742410  3.06213070462171047818
-0.80901699437494742410  1.80901699437494742410  0.80901699437494742410  1.89250085345088179814
 0.00000000000000000000  3.06213070462171047818  1.89250085345088179814  3.73606797749978969641

-0.30901699437494742410  0.50000000000000000000  0.80901699437494742410  0.00000000000000000000
-0.50000000000000000000  2.61803398874989484820 -1.80901699437494742410  3.06213070462171047818
-0.80901699437494742410 -1.80901699437494742410  0.80901699437494742410 -1.89250085345088179814
 0.00000000000000000000  3.06213070462171047818 -1.89250085345088179814  3.73606797749978969641

-0.30901699437494742410 -0.50000000000000000000 -0.80901699437494742410  0.00000000000000000000
 0.50000000000000000000  2.61803398874989484820 -1.80901699437494742410 -3.06213070462171047818
 0.80901699437494742410 -1.80901699437494742410  0.80901699437494742410  1.89250085345088179814
 0.00000000000000000000 -3.06213070462171047818  1.89250085345088179814  3.73606797749978969641

-0.30901699437494742410  0.50000000000000000000 -0.80901699437494742410  0.00000000000000000000
-0.50000000000000000000  2.61803398874989484820  1.80901699437494742410 -3.06213070462171047818
 0.80901699437494742410  1.80901699437494742410  0.80901699437494742410 -1.89250085345088179814
 0.00000000000000000000 -3.06213070462171047818 -1.89250085345088179814  3.73606797749978969641

 2.61803398874989484820  1.80901699437494742410  0.50000000000000000000  3.06213070462171047818
 1.80901699437494742410  0.80901699437494742410 -0.80901699437494742410  1.89250085345088179814
-0.50000000000000000000  0.80901699437494742410 -0.30901699437494742410  0.00000000000000000000
 3.06213070462171047818  1.89250085345088179814  0.00000000000000000000  3.73606797749978969641

 2.61803398874989484820 -1.80901699437494742410  0.50000000000000000000 -3.06213070462171047818
-1.80901699437494742410  0.80901699437494742410  0.80901699437494742410  1.89250085345088179814
-0.50000000000000000000 -0.80901699437494742410 -0.30901699437494742410  0.00000000000000000000
-3.06213070462171047818  1.89250085345088179814  0.00000000000000000000  3.73606797749978969641

 2.61803398874989484820 -1.80901699437494742410 -0.50000000000000000000  3.06213070462171047818
-1.80901699437494742410  0.80901699437494742410 -0.80901699437494742410 -1.89250085345088179814
 0.50000000000000000000  0.80901699437494742410 -0.30901699437494742410  0.00000000000000000000
 3.06213070462171047818 -1.89250085345088179814  0.00000000000000000000  3.73606797749978969641

 2.61803398874989484820  1.80901699437494742410 -0.50000000000000000000 -3.06213070462171047818
 1.80901699437494742410  0.80901699437494742410  0.80901699437494742410 -1.89250085345088179814
 0.50000000000000000000 -0.80901699437494742410 -0.30901699437494742410  0.00000000000000000000
-3.06213070462171047818 -1.89250085345088179814  0.00000000000000000000  3.73606797749978969641


